NLO QCD bottom corrections to Higgs boson production in the MSSM
G. Degrassi
1
P. Slavich
0
0
LPTHE, 4, Place Jussieu, F-75252 Paris,
France
1
Dipartimento di Fisica,
Universita` di Roma Tre and INFN
, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome,
Italy
We present a calculation of the two-loop bottom-sbottom-gluino contributions to Higgs boson production via gluon fusion in the MSSM. The calculation is based on an asymptotic expansion in the masses of the supersymmetric particles, which are assumed to be much heavier than the bottom quark and the Higgs bosons. We obtain explicit analytic results that allow for a straightforward identification of the dominant contributions in the NLO bottom corrections. We emphasize the interplay between the calculations of the masses and the production cross sections of the Higgs bosons, discussing sensible choices of renormalization scheme for the parameters in the bottom/sbottom sector.
Contents
1 Introduction 2 3 4
Higgs boson production via gluon fusion at NLO in the MSSM
Outline of the calculation
Two-loop bottom/sbottom contributions
4.1 Contributions controlled by the Higgs-bottom coupling
4.2 Contributions controlled by the Higgs-sbottom coupling
4.3 On-shell renormalization scheme for the sbottom parameters
A numerical example
Conclusions and discussion
A NLO contributions from real parton emission
B Renormalization scheme shifts in the sbottom sector
Introduction
With the coming into operation of the Large Hadron Collider (LHC), a new era has begun
in the search for the Higgs boson(s). At the LHC the main production mechanism for the
Standard Model (SM) Higgs boson, HSM, is the loop-induced gluon fusion mechanism [1],
gg HSM, where the coupling of the gluons to the Higgs is mediated by loops of colored
fermions, primarily the top quark. The knowledge of this process in the SM includes the
full next-to-leading order (NLO) QCD corrections [25], the next-to-next-to-leading order
(NNLO) QCD corrections [611] including finite top mass effects [1218], soft-gluon
resummation effects [19], an estimate of the next-to-next-to-next-to-leading order (NNNLO)
QCD effects [20, 21] and also the first-order electroweak corrections [2228].
The Minimal Supersymmetric extension of the Standard Model, or MSSM, features
a richer Higgs spectrum which consists of two neutral CP-even bosons h, H, one neutral
CP-odd boson A and two charged scalars H. The gluon-fusion process is one of the most
important production mechanisms for the neutral Higgs bosons, whose couplings to the
gluons are mediated by colored fermions and their supersymmetric partners. The
gluonfusion cross section in the MSSM is known at the NLO. The contributions arising from
diagrams with squarks and gluons were first computed under the assumption of vanishing
Higgs mass in ref. [29]. The complete top/stop contributions, including stop mixing and
gluino effects, were computed under the same assumption in ref. [30, 31], and the result
was cast in a compact analytic form in ref. [32]. Later, more refined calculations aimed
at the inclusion of the full Higgs-mass dependence. In particular, the full squark-gluon
contribution is known in a closed analytic form [3335], while the full quark-squark-gluino
contribution has been computed in ref. [36] via a combination of analytic and numerical
methods.
It should be stressed that, at least for the case of the light Higgs, the exact
twoloop QCD Higgs-gluon-gluon amplitude is in general well approximated by the amplitude
evaluated in the limit of neglecting the Higgs mass. The latter is much easier to compute
and the corresponding result can be straightforwardly implemented in computer codes that
aim to evaluate the Higgs boson production cross section in a fast and efficient way. Indeed,
it was noticed several years ago for the SM case [37] that the exact K factor, defined as
the ratio between the NLO and leading-order (LO) cross sections, is well approximated
by the so-called effective K factor that can be obtained via an improved effective-theory
calculation. By the latter we mean a result in which the effective NLO cross section is
obtained by multiplying the exact LO partonic cross section by the O(s) corrections
evaluated in the limit of vanishing Higgs mass. For the SM case this approximation works
at the level of few per cent for Higgs mass values below the 2 mt threshold, and up to 10%
for any Higgs mass value. The same level of accuracy is reached when the Higgs couples
to a generic scalar particle with mass mS, with the exception of a narrow region close to
the mH 2 mS threshold [38].
There is only one case in which the effective approximation does not work sufficiently
well, namely when the bottom contribution becomes very relevant. This can happen in
the MSSM when tan , i.e. the ratio of the vacuum expectation values (vev) of the neutral
components of the two Higgs doublets, becomes large. In such a situation, in principle,
the exact computation of the NLO bottom contribution to the cross section should be (...truncated)